<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: CONNSP_1:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">GX</font> being   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">F</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Olive" title="b1">GX</font>  st (  for <font color="Olive" title="b3">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">GX</font>  st <font color="Olive" title="b3">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">F</font> holds <br/><font color="Olive" title="b3">A</font> is  <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>  ) &amp;  ex <font color="Olive" title="b3">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">GX</font> st <br/>( <font color="Olive" title="b3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Olive" title="b1">GX</font> &amp; <font color="Olive" title="b3">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">F</font> &amp; (  for <font color="Olive" title="b4">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">GX</font>  st <font color="Olive" title="b4">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">F</font> &amp; <font color="Olive" title="b4">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">A</font> holds <br/> not <font color="Olive" title="b3">A</font>,<font color="Olive" title="b4">B</font> <a href="connsp_1.html#R1" title="CONNSP_1:pred.1">are_separated</a>  ) ) holds <br/> <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Olive" title="b2">F</font> is  <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> </div></div>
